"Source: Text/Incidence/Design.text";
"Line: 2460";
"Date: Fri Sep 26 12:10:10 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Incidence/Design.text, line: 2460
// Example: H160E11 ()
print "Example: H160E11";
ei := GetEchoInput();
SetEchoInput(true);
D, P, B := WittDesign(12);
A, PY, BY := AutomorphismGroup(D);
A;
a := A!(1, 2, 3, 4)(5, 6, 12, 11);
4^a;
assert $1 eq 1;
{1, 2, 3}^a;
Image(a, BY, Block(D, 3));
S2 := SylowSubgroup(A, 2); 
S2;
Stabilizer(S2, BY, Block(D, 4));
Stabilizer(S2, 6);          
3^S2;
IsPointTransitive(D);
assert $1;
IsBlockTransitive(D); 
assert $1;
H := ActionImage(A, BY);
#H;
assert $1 eq 95040;
H;
SetEchoInput(ei);
